Abstract
In this paper we the study of dynamics of time since infection structured vector born model with the direct transmission. We use standard incidence term to model the new infections. We analyze the corresponding system of partial differential equation and obtain an explicit formula for the basic reproduction numberℜ0. The diseases-free equilibrium is locally and globally asymptotically stable whenever the basic reproduction number is less than one,ℜ0< 1. Endemic equilibrium exists and is locally asymptotically stable whenℜ0> 1. The disease will persist at the endemic equilibrium whenever the basic reproduction number is greater than one.
Highlights
Zika virus (ZIKV) is a flavivirus, transmitted by the Aedes aegypti mosquitoes as for the other vector borne diseases such as malaria, dengue fever, and West Nile virus
Between 2007 and 2016, the spread of Zika virus infections have been reported around the world, including in southeast Asia; French Polynesia and other islands in the Pacific Ocean; and parts of South, Central, and North America [6, 12, 22]
We present a mathematical model of ZIKV incorporating both vector and direct transmission where infected individuals are structured by time-since infection
Summary
Zika virus (ZIKV) is a flavivirus, transmitted by the Aedes aegypti mosquitoes as for the other vector borne diseases such as malaria, dengue fever, and West Nile virus. Zika infection during pregnancy can cause serious birth defects and ZIKV infections were found to be connected with Guillain-Barre syndrome and Microcephaly [5, 29]. Several mathematical models have been used to understand the transmission dynamics of vector borne diseases [3, 7, 27, 37, 39,40,41]. We present a mathematical model of ZIKV incorporating both vector and direct transmission where infected individuals are structured by time-since infection.
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